Bound Definition and 476 Threads

Bekenstein bound states that the amount of information in some region of the space is proportional to the surface of the region, not the volume. Cauchy's integral formula states that for any holomorphic function on a complex plane inside some region defined by a closed curve the values of...

Hello everyone. I was yesterday asked in an interview to draw a gaussian curve. I drew. And then they asked in what region would this give rise to bound states? I am really confused how to conclude if a function gives bound state or not. Please help. Thanks.

Homework Statement Given the potential V(x) = - 1/ sqrt(1+x^2) Consider this in a 50x50 matrix representation of the hamiltonian in the basis of a one dimensional harmonic oscillator. Determine the eigenvalues and eigenvecotrs, the optimal parameter for the basis, and cop ate the...

Hello readers, Given the potential V(x) = - 1/ sqrt(1+x^2) I have found numerically 12 negative energy solutions Now I want to try to solve for these using matrix mechanics I know the matrix form of the harmonic oscillator operators X_ho, P_ho. I believe I need to perform the...

Homework Statement Find, with proof, the least upper bound of the set of real numbers E given by: E ={14n + 9/16n + 13: n \in N}  : Homework Equations The Attempt at a Solution So I said that 16n+13>14n+9 for all N From this I get n>-2 What do I do with this? I...

Homework Statement Find surface and volume charge densities. Deduce electric field. Homework Equations The Attempt at a Solution Volume charge density: \epsilon_0 \epsilon_r \nabla . \vec E = \rho_f Using ##\vec P = \chi \epsilon_0 \vec E = (\epsilon_r -1)\epsilon_0 \vec E##...

Hello Forum, in the case of two or multiple free vectors, it is easy to determine graphically (head-tail rule) the resultant vector (magnitude and direction). The resultant vector is also a free vector. A free vector is actually an infinite number of vectors with the same magnitude and...

A function ##f:\mathbb{R}^3_+\to[0,1]## defined as ##f(\lambda,\beta,x)=1-e^{-\frac{\lambda}{\beta}\left(1-e^{-\beta x}\right)}## serves a lot of pain under integration. As this function is used to describe a lower bound, could anyone suggest another non-zero function that would be smaller than...

Homework Statement Introduction to Classical Mechanics by David Morin - problem 9.43, page 424 A uniform flat rectangular sheet of mass m and side lengths a and b rotates with angular speed w around a diagonal. What torque is required? Given a fixed area A, what should the rectangle look...

Homework Statement I am studying my lecturer's notes and in this part he uses a delta potential to illustrate a simple example of Fermi's golden rule, that the rate of excitation is ##\propto t##. Homework Equations The Attempt at a Solution I've managed to get the bound states, by solving...

Homework Statement if the series ∑(n=1, goes to infinity) (-1)^n/(n^3) is approximated by its ninth partial sum, find a bound for truncation error Homework Equations Alternating Series Estimation Thm: If alternating series is CONVERGENT, then truncation error for nth partial sum is less than...

Hi PF. This a fact well aware to just about anyone that has had even basic chemistry, but I'm having a hard time coming to an understanding as to why this must be true. So why? Also, if I knew that some box contained, say, a proton and an electron, could I ever know whether or not, inside...

Homework Statement Let A be a non-empty subset of R (real numbers) and a an upper bound in R for A. Suppose that every open interval I containing a intersects A (so the intersection is non-empty). Show that a is a least upper bound for A. The Attempt at a Solution I've seen the prettier...

Homework Statement Given the delta function -α[δ(x+a) + δ(x-a)] where α and a are real positive constants. How many bound states does it possess? Find allowed energies for \frac{hbar2}{ma} and \frac{hbar2}{4ma} and sketch the wave functions. Homework Equations I know there are three parts of...

FORTRAN error "array bound is not scalar integer" I'd like to know if a loop can be created, inside which I can call a subroutine in which there are arrays to be defined whose size varies as a function of loop variable. I tried as following, but got error "array bound is not scalar integer"...

Hi, I wonder if there is an elegant way of how to picture (or describe at all) the transition of free electrons (non-quantized, point-like charges) into let's say the bound ground state of the hydrogen atom (in which it becomes quantized and cloud-like). How does the transition occur ? When...

Hello! :) I am looking at the following exercise: Let the linear system $Ax=b$ with $\begin{pmatrix} 2.001 & 2\\ 2& 2 \end{pmatrix}$ ,$b=\begin{bmatrix} 2.001 &2 \end{bmatrix}^T$ and y an approximate solution,so that $Ay-b=\begin{bmatrix} 0.001 &0 \end{bmatrix}^T$ .Find an upper bound of the...

Hello everyone, I have a large number of measurements with associated uncertainties, and I know that the real values are bounded above by some constant. How can I estimate the value of that constant, and the uncertainty on the estimate? Thanks

I was reading my quantum mechanics text and I have a doubt. I have the energy levels well defined for the finite square well and the author suddenly compares (I believe) those levels with the levels of the nucleon with the following phrase: "is the spacing between levels on the order of MeV for...

If |a_{mn}x_0^my_0^n| \leq M then a double power series f(x,y) = \sum a_{mn} x^m y^n can be 'bounded' by a dominant function of the form \phi(x,y) = \tfrac{M}{(1-\tfrac{x}{x_0})(1-\tfrac{y}{y_0})}, obviously derived from a geometric series argument. This is useful when proving that analytic...

What is the physical meaning to a bound state with negative energy? As I understand it, this is the case with the delta function potential, which admits only one bound state with a negative energy. If the potential function is identically zero throughout (except at the delta function peak)...

Homework Statement Consider a potential function V(x) such that: $$ \begin{cases} V(x)\leq 0\text{ for }x\in[-x_0,x_0] \\ V(x)=0 \text{ for }x\not\in[-x_0,x_0] \end{cases} $$ Show, using the variational method that: (a) In the 1-dimensional case \lambda^2V(x) always possesses at...

Hi, Homework Statement A particle of mass m has a potential V(r)= -Vo r<a 0 r>a Find the minimum value of Vo for which there's a bound state of energy and angular momentum are zero by solving shrodinger equation for E<0 and taking the limit E-> 0 Homework Equations The Attempt...

Homework Statement A certain coaxial cable consists of copper wire, radius a, surrounded by a concentric copper wire of outer radius b. The space between is filled with a dielectric with a relative permittivity of \epsilon_{r} = \frac{s}{a}, a \leq s \leq b Find the bound charges by using two...

Given [a,b] a bounded interval, and f \in L^{p} ([a,b]) 1 < p < \infty, we define: F(x) = \displaystyle \int_{a}^{x} f(t) dt, x \in [a,b] Prove that exists K \in R such that for every partition: a_{0} = x_{0} < x_{1} < ... < x_{n} = b : \displaystyle \sum_{i=0}^{n-1} \frac{| F(x_{i+1}) -...

Homework Statement The space between the plates of a parallel plate capacitor is filled with a dielectric material whose dielectric constant ϵr varies linearly from 1 at the bottom plate (x=0) to 2 at the top plate (x=d). The capacitor is connected to a battery of voltage V. Find all the bound...

MODERATOR'S NOTE: problem statement is mistaken, please see https://www.physicsforums.com/showthread.php?t=723342 Homework Statement The space between the plates of a parallel plate capacitor is filled with a dielectric material whose dielectric constant $\epsilon_r$ varies linearly from 1 at...

Homework Statement Show in the graph ,there will be no allowed bound states with odd-parity if the well depth is less than ${V_min}$ Find ${V_min}$ in terms of k and a.where a is the half of the well width. What does no allowed bound state mean? Homework Equations $cotz=-pa/z$ where p^2...

Reading from http://quantummechanics.ucsd.edu/ph130a/130_notes/node150.html Again we have assumed a beam of definite momentum incident from the left and no wave incident from the right. Why is the above statement made? What does the reflected wave mean? There is now all why reflected...

Hello, I am not quite certain if I have properly placed this query in the correct forum. I am currently reading this article on dark matter http://pdg.lbl.gov/2013/reviews/rpp2012-rev-dark-matter.pdf In the first paragraph, the author states, "This leads to a lower bound on the DM mass...

Hi folks -- quick question. I appreciate that entangled states in quantum mechanics may not be bound states. But when we have bound states, are the particles always entangled with one another? Thanks a lot!

Hi, I just need to ventilate and see your opinions. Charge can be partitioned into groups of particles of one or more elements. If they have more than one element it is a molecule, and its position is represented by for example the center of mass, seeing each particle as carrying both the...

In the double delta function potential well, where one delta function ( -αδ(x) ) is at -a and one at +a, if the energy is less than zero, there can be either one or two bound states, depending on the magnitude of α...if α is large enough, there can be two bound states, but if α is small, there...

With great interest I read an article about a paper where scientists were able to create two photon bound states ("molecules of light"). http://physicsworld.com/cws/article/news/2013/sep/26/physicists-create-molecules-of-light I was quite astonished since light normally does not...

Is there a way to know qualitative information about energy spacing of bound state energy? Infinite square well. V=0 -a/2<x<a/2 V=∞ otherwise Bound state energy E\propto n^2 space beteween succesive energies increases at higher energy (n+1)^2-n^2=2n+1 Harmonic Oscillator V\proptox^2 E\propto...

Let f = ln(\frac{1}{1-x}) show that if x \in [-1/2 , 1/2] then |f^{n+1}(x)| <= 2^{n + 1} * n! I am having a hard time seeing how 2^{n + 1} * n! comes into play. I have that the taylor series for f is \Sigma \frac{x^n}{n} If a take a derivative it becomes x^(n-1) and...

In Griffith's EM text, he devouts 2 pages to deriving the equation for bound currents, and for the next 4 problems, he (the solution manual) doesn't even use the equations just introduced. I question the wisdom of deriving an equation that is harder to work with than we already had...

Suppose you flip a fair coin 10,000 time how can you characterize the distribution of the occurrence of head? From the textbook, it says that P[head>n/2 + k√n] < e^(-k^2)/2, why is that and what is the derivation? What theorem is this, we had only learn Bernoulli distribution and Chebyshev so...

The potential due to a polorized distribution is given by: V( \vec{r}) = \frac{1}{4 \pi \epsilon _{0}} \int _{V} \frac{ \hat{r} \cdot \vec{P} ( \vec{r}')}{r^{2}} dV After working some voodoo math, this is worked into the form V = \frac{1}{4 \pi \epsilon _{0}} \oint _{S} \frac{1}{r} \vec{P}...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Homework Statement "The Michelson-Morley experiment was conducted using an interferometer with L1 = L2 = 40m, lambda = 632nm, and maximum fringe separation d = 0.0022 fringes. Find the upper bound on the relative speed of the Earth and the ether, and clearly state the significance of the...

Studying the movement of a particle on bound orbits around a black hole I found a fact that seemed a little strange for me -- that on these orbits particle's total energy on infinity must be less than unit (E<1). As far as I understrand, it is not so horrible, since here we deal with an...

Hi all; I need some clarification in red part; in how it is deduced from the theorem 2.5.6! I know how the blue is deduced from the theorem but don't even know how to get blue form red in practice!(No algorithm is suggested...) Anyway, any explanation is thanked... Regards.

At: http://en.wikipedia.org/wiki/Upper_and_lower_bounds in example it says that "2 and 5 are both lower bounds for the set { 5, 10, 34, 13934 }, but 8 is not" Why "2"? as 2 is not in that set. Also, at: http://en.wikipedia.org/wiki/Supremum in example it says that "The...

The result of the Kallen-Lehmann spectral representation is that the two point correlation (and thus also the full propagator) has a pole in the physical mass of the particle. In Peskin and Schroeder it is also argued that multiparticle states show up as a cut, but bound states can also show up...

I am struggling to draw this point home: To prove that R has LUB property, we used the following reasoning: First we defined R to be set of cuts (having certain properties) where each cut corresponds to a real number and then we proved any subset A of R has LUB (least upper bound) property...

On one side, the amount of information is bounded above for any fixed volume of space: this would seem (?) to indicate that information content is local. Yet physical states are not necessarily local, as non-local entanglement shows. So how do you have local information content of a non-local...

Homework Statement Calculate the value of n so that the approximation is within 0.0001. b = 2, a = 1. f(x) = 1/x. Homework Equations f4(x) = 24/x^5 (Think this is correct) Error <= (b-a)^5/180n^4(MAXx [a,b](f4(x)) The Attempt at a Solution Well, 24/x^5 obtains it's max at x =1...

A couple of quick questions after watching a video on the helectic model that the solar system follows on it's course around the galactic center. Please bare with me these maybe idiotic questions. A) Are black holes bound to the spin of the galaxy or do they sit in place on the galactic plane...

Hi guys I have a doubt. How can I prove that (∫ (from 0 to pi) sin^7 xdx)(∫ (from 0 to pi) sin^(7/6) xdx)^6 is at most 128 But how can I prove that the lower bound of this expression is (pi/2)^7I think is a very interesting and not an easy question so any ideas? A guidance or something...